Stop worrying and have fun. Your truck will hardly know that little light trailer is behind it. I have the same truck and tow a 31' 7600lbs tt. I pulled several long 10+ percent grades this summer on a 2k mile trip without any issue. Put it in "tow" mode and put the shifter in manual 5th gear (s mode) which will lock out 6th gear and stop it from hunting. Don't be afraid to let it drop a gear or 2 and rev. Power has never been an issue.
The 5.7l comes equipped with a trans cooler and stock 4.30 rear gears for towing.